The present invention relates to seismic exploration and more particularly, relates to the processing of seismic exploration data to enhance seismic signals resulting from the conversion of compressional waves (P-wave) to shear waves (S.sub.v -wave), or shear waves to compressional waves, upon reflection from contrasts or differences in elastic properties in the earthen subsurface.
Conventional compressional wave seismic land or marine acquisition techniques involve the use of an appropriate source to generate compressional energy and a set of receivers spread out along or near the earthen surface to detect any seismic signals due to compressional energy being reflected from subsurface geologic boundaries. These signals are recorded as a function of time and subsequent processing of these signals, i.e. seismic data, is designed to reconstruct an appropriate image of the subsurface. In simplistic terms, this conventional process has a compressional wave travelling down into the earth, reflecting from a particular geologic layer (impedance contrast), and returning to the receiver as a compressional wave. Data from such a process is denoted herein as "PP" data since a compressional wave (P) goes down from the surface (1st P) and back up to the surface (2nd P); for water covered areas this may be a "PPPP" process since compressional waves are also relied on both in the water and in the earth. In reality, many different types of waves are created in this conventional acquisition scheme and the use of receivers with their sensitive axes oriented vertically (approximately parallel to particle motion for compressional waves), as well as the subsequent processing of the recorded data are designed so that the desired type or types of waves (such as signals representing PP data) is enhanced relative to other types of waves whose signals are considered noise.
Shear wave data is conventionally acquired by using a source which introduces particle motion transverse to the desired direction of wave propagation and then detecting the seismic signal with receivers whose sensitive axes are oriented horizontally. Two different types of shear waves (denoted herein as "S") may be acquired: S.sub.h, where the particle motion is perpendicular to, or across, the line from the source to the receiver or geophone; and S.sub.v, where the particle motion is along, or in, the plane defined by the source, reflector, and receiver or geophone. While the characteristics and interpretation of these two types of shear waves may be quite different, both types of acquisition are denoted herein as SS to emphasize the symmetry resulting from the fact that both the downgoing wave (1st S) and reflected wave (2nd S) are shear waves. Shear seismic data may provide additional information about the properties of the subsurface geologic layers which may be valuable in the exploration for hydrocarbons ("V.sub.P /V.sub.S -- A Potential Hydrocarbon Indicator", Geophysics 41, pp. 837-849 (1976) Tatham, R. H. and Stoffa, P. L.).
Shear waves of the S.sub.v type may also be generated by conversion from a compressional wave transmitted through or reflected from an appropriate interface. In the converted shear case the particle motion of the converted wave is transverse to the direction of wave propagation but in-line with respect to the source-receiver direction. These waves may be seen in conventional PP seismic records but their observation can be enhanced by modifying the conventional compressional wave acquisition geophone axes slightly (i.e. placing geophones with their detection axes horizontally in-line rather than vertical). Seismic signals which are predominantly shear-waves may then be detected and may also be recorded. These waves are created by the partitioning of the energy of the compressional wave as it is reflected from an elastic interface. Shear waves of this type are called converted waves, or PS waves, and are well known among exploration seismologists ("Composite Reflections", Geophysics 15, pp. 30-50 (1950) Ricker, N. and Lynn, R. D.; see also U.S. Pat. No. 2,354,548, issued July 25, 1944 to Ricker). When properly interpreted they may provide information about the properties of the subsurface that is quite similar to that provided by SS data. Converted waves of the SP type (i.e. shear wave generated at the source travelling down and converting to a P-wave upon reflection) may also be acquired and will have the same properties as a PS converted wave with an interchange of source and receiver positions and names.
There are two characteristics of converted waves (PS or SP) which distinguish them from either conventional PP or SS waves. First, the travel path is asymmetric; compressional energy travels downward with a compressional velocity V.sub.P (Z), and after reflection travels upward with a shear velocity V.sub.S (Z). V.sub.P (Z) and V.sub.S (Z) are both generally functions of depth, Z, and V.sub.S is normally much less than V.sub.P. Second, since the shear velocity is usually much smaller than the compressional velocity in the same material, the velocity distribution (i.e. the velocities experienced by the energy travelling down and back up) of a converted wave is much broader than if the wave had been a pure compressional (PP) or pure shear (SS) wave over its entire path. To understand how these two characteristics affect the basic conventional processing methods of velocity analysis and the so-called common midpoint stack (which are designed to enhance seismic signals), these basic conventional processing methods will be briefly discussed for PP and SS data.
The earth model utilized herein for this discussion of the analysis of basic processing methods or strategy is one for which velocities vary with depth due to layering, but not laterally. The seismic reflection from an interface in such a stratified medium will arrive at the receiver at a time, defined and used herein as T(X), where X is defined and used herein as the distance between the source and the receiver, or "offset" distance. This "moveout time" T(X) may be used to "dynamically correct" seismic data acquired at an offset distance X so that the data appears as if it had been acquired at zero offset, i.e. X=0. Further, the square of this moveout time has a well known expansion about EQU T.sup.2 (X)=T.sub.0.sup.2 +a.sub.1 X+a.sub.2 X.sup.2 +a.sub.3 X.sup.3 +a.sub.4 X.sup.4 + . . . (1)
where the coefficients a.sub.i are moments of the normal propagation (interval) velocity. For the case of horizontal reflectors all of the odd terms must be zero by symmetry since interchanging source and receiver positions, which corresponds to a change in the sign of the offset distance X, will necessarily have the same travel time. Experience with compressional wave (PP) data has indicated that the P-wave vertical velocity distributions are such that, in most areas, within the offset range (X&lt;2Z), and frequency ranges (5-100Hz) normally considered in exploration seismology, terms higher than X.sup.2 may be ignored. That is, deviations from the so called "normal hyperbolic moveout" (NMO) are minimal compared to other errors. This is equivalent to approximating the stratified earth with a single horizontal layer, having an "effective" velocity, V.sub.e. For this simplified case Equation 1 reduces to the familiar hyperbolic moveout expression ##EQU1##
If the reflector of interest is not horizontal but is angled or dipping then this analysis and the equations become somewhat more complicated. While velocities may still be uniform laterally, for dipping reflectors it becomes necessary to specify a particular point in the model about which moveout analysis is being considered. The depth to the reflector is specified by the distance from the point to the surface along a line that is normal to the reflector at that point and extends to the surface.
Conventional processing of PP or SS data gathers the data by the common mid-point (CMP) technique and relies on symmetry to use the "mid-point" between the source (S) and receiver (R) positions as a surface gather point, as seen in FIGS. 1A and 1B. That is, after the data have been acquired for a number of sequential source positions they are sorted or gathered into different midpoint groups which have the same or "common" surface location of one "midpoint" between the various source and receiver positions. The motivation for a CMP sort or gather for PP or SS data is two-fold. First a CMP sort corresponds to all ray-paths for this gather having a common reflection point (CRP) in the subsurface, if the reflectors are horizontal; thus, this sort minimizes the lateral smear of the horizontal events in stacked data resulting from this sort. Second, and probably more important, the common midpoint sort causes the odd power terms in the moveout time expression given by Equation 1 to be zero for PP and SS events, even for dipping reflectors. This is easily shown to be true by symmetry, since sources and receivers may be interchanged, thus changing the sign of the offset distance, with no change in the overall raypath.
In summary, common midpoint processing of PP and SS data using the hyperbolic (Equation 2) moveout analysis works because:
(1) the vertical velocity distributions are generally narrow enough that higher order terms are not significant for the standard offset ranges and frequency bands considered in exploration seismology;
(2) the raypath source/receiver symmetry insures that all odd-order terms will be zero; and
(3) the reflection point lateral smear associated with common midpoint sorting is negligible for small dip angles, and is of less concern than moveout analysis errors.
Converted wave data meet none of these three conditions. The fact that shear velocities are significantly smaller than P-wave velocities, often by a factor of two or more, creates a very broad total velocity distribution which causes the higher order terms in the moveout expression of Equation 1 to be significant even at the moderate offset distances used in seismic exploration employing converted waves. The asymmetry of the ray-path, as shown in FIG. 1C, down with velocity V.sub.P and up with velocity V.sub.S, causes the odd order terms to be non-zero for dipping reflectors, and in fact these terms are quite significant. The reflection point for PS data is not the midpoint between source and receiver positions even for horizontal reflectors, but varies with both offset distance and depth even for a constant velocity model (i.e. V.sub.P (Z)=V.sub.1 and V.sub.S (Z)=V.sub.2, both V.sub.1 and V.sub.2 constant); similarly, for SP data the reflection point is not the midpoint, as shown in FIG. 1D.
There are two additional physical aspects which have much greater significance for PS data than for PP or SS. First, the reflection (conversion) coefficient for PS seismic events is always zero at normal incidence and for small incidence angles increases as the sine of the incidence angle. The behavior of the reflection coefficient at large angles (long offsets) depends on the elastic properties of the media on each side of the reflecting interface, as does the behavior of PP, S.sub.h S.sub.h, or S.sub.v S.sub.v reflection coefficients. The important difference is that while stacking PP and SS data may be thought of as an attempt to enhance the normal incidence signal, this is not the case for PS data because there is no normal incidence signal. Thus, processing and interpretation procedures which are based on derivations using small angle assumptions may be perfectly suitable for PP and SS data, but may be totally inadequate for converted wave data.
Second, velocity anisotropy plays a more fundamental role in PS processing than in PP or SS. For the layered earth model, the velocity field is transversely isotropic with the axis of symmetry perpendicular to the surface. For transversely isotropic media pure compressional (P) and pure shear (S.sub.v) modes occur only along the axis of symmetry. Off this axis, these modes are mixed and are referred to as pseudo-P and pseudo-S.sub.v. When the terms "P" and "S" modes (or waves) are used herein in the presence of anisotropy, these terms mean the appropriate "pseudo" mode (or wave).
The velocity anisotropy of a transversely isotropic elastic medium may be completely characterized by the density (p) and five independent elastic constants for that medium; these constants are normally C.sub.11, C.sub.12, C.sub.13, C.sub.33 and C.sub.44. Thus, is these elastic constants and density are known or specified, the P, S.sub.h, and S.sub.v velocities may be determined for any direction of wave propagation. Alternatively one can completely characterize the velocity field by specifying the vertical velocities and the apparent anisotropy factors A.sub.Sh, A.sub.P *, A.sub.Sv * ("Velocity Anisotropy of Seismic Waves: Field Observations", S.E.G. 1983 Annual Meeting Extended Abstracts (1983) Sriram, K. P., Fulton, T. W., Nooteboom, J. J. and Seriff, A. J.). For example, some equations for such an alternate characterization are, ##EQU2## These anisotropy factors represent the coefficients of an elliptical fit to the velocity function V(.theta.) at normal incidence. That is, these parameters are coefficients derived from matching an elliptical asymptotic limit (.theta. going to zero) to the correct wavefront and, they uniquely determine the necessary combinations of elastic constants required to calculate the true wavefront at all angles.
Generalizing equations 3a and 3b to include the case of transverse isotropy, as well as the case where the downward and upward propagating waves have different velocities (i.e. PS or SP), gives, ##EQU3## For the case of horizontal layers is the coefficient of the quadratic term in the moveout time expansion in equation 1.
The apparent horizontal velocity, V.sub.h *=A*V.sub.V, (where V.sub.V is vertical velocity) is the quantity which is deduced from normal moveout velocity analysis using offset ranges normally encountered in conventional exploration seismology. While the difference between apparent horizontal and vertical velocity is important for converting from travel time to depth for seismic data display and interpretation, the explicit inclusion of anisotropy is generally not important for the proper dynamic (NMO) correction of PP and SS seismic data (in the limits normally encountered in exploration seismology).
For PS (or SP) data this is not the case for several reasons. First, S.sub.v -wave apparent anisotropy factors can be quite large compared to P-wave anisotropy factors. Second, the P-wave angles of incidence encountered in PS seismic data acquisition will generally be much larger than those encountered in PP seismic data acquisition. Third, since dipping reflectors have a significant effect on PS travel time determination, it is important to be able to measure these dip angles from the seismic section, which requires a knowledge of the anisotropies involved (similar to time-to-depth conversion for PP seismic data).
Many successful methods for moveout (NMO) velocity analysis and dynamic correction of PP and SS seismic data have been in use since the late 1960's. The display techniques which are used herein are similar to those developed over the years for use with conventional hyperbolic velocity analysis, as described for instance by Taner and Koehler ("Velocity Spectra-Digital Computer Derivation And Applications Of Velocity Functions", Geophysics 34, pp. 859-881 (1969) Tanner, M. T. and Koehler, F.).
The need for an improved method to dynamically correct (NMO) PS seismic data has been recognized by Dohr and Janle ("Improvements In The Observation Of Shear Waves", Geophysical Prospecting 28, pp. 208-220 (1980) Dohr, G. and Janle, H.) who proposed using a double quadratic expression for the moveout function T(X) which would properly correct PS data for a horizontal reflector if one were able to determine the appropriate V.sub.P and V.sub.S, as well as the reflection point. However, they did not describe a method for determining the velocities from the seismic data, account for the possibility of dipping reflectors, nor account for anisotropy.
These and other limitations and disadvantages of the prior art are overcome by the present invention, however, and improved methods are provided for determining fractional sort point gathers, dynamic corrections, estimates of interval velocities from effective velocities, and better stacked sections resulting therefrom.